The Monaco striker spent last season on loan at Manchester United but he has joined Chelsea for the forthcoming campaign.
Terry revealed that Falcao gave him a torrid time when Chelsea faced United in April last season, and from what he has seen in instruction through pre-season, the Blues skipper is predicting huge things.
"His movement is unbelievable and actually two minutes in to the game we played against Manchester United last season I turned to Gaz (Cahill) and mentioned 'we have to be on it today'.
"After two minutes he'd given me an elbow, he was backing into me, he was coming short, running in behind - he wouldn't leave me alone. He was up for it.
"Now I have noticed him initial hand in coaching every day and his finishing is unbelievable. I consider if he gets a run within the side he can reproduce his type in the previous.
“His profession has been all about targets and scoring targets on the large occasion so I’m hoping which is what he brings for the side. He wants to succeed and no doubt that is why he has come to us
“He desires us to win items and if we are to win things he is going to possess to score a lot of goals. We're hoping that it's a fantastic mixture and he does seriously well for us.”
Terry expects a further challenging battle for the Premier League title, but says that Chelsea’s greatest asset is their manager, Jose Mourinho.
"To improve upon what he was is some task but I’ve noticed him make slight improvements all over,” he said. “When that you are speaking about the very ideal improving you will find only slight improvements it is possible to make and he's the really ideal.
"We are extremely fortunate to possess him. He pushes us every day. He hates losing along with the intensity is one hundred per cent. In the event you do not give every little thing you will not match into his regime and that is why we have seen players come and go over the years such as massive players.
"His desire to win on a daily basis and that hunger is what sets him apart from everybody."